The Existence Of A Positive Solution To A Class Of Quasilinear Elliptic Equation In R~N

In this paper, we consider the following quasilinear elliptic equation on RN where f€C1(R+, R) is subcritical,N> p>2.Since Sobolve imbedding W1P(RN)�'Lq(RN)(p≤q<p*) is noncompact on RN,the (P.S.) condition is difficult to proof. We will use the method of penalization methods to give a sequence which satis-fies the (P.S.) condition. Then we prove that under some conditions on f(u),the problem has positive solution.